Final exam for precalculus

The standard form of the equation of a circle is $$(x-h)^2 + (y-k)^2 = r^2$$ , where (h, k) is the center and r is the radius.

To convert radians to degrees, multiply the radian measure by $$\frac{180}{\text{π}}$$ .

A conic section is a curve obtained by intersecting a cone with a plane. The types include circles, ellipses, parabolas, and hyperbolas.

The standard form of the equation of an ellipse is $$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$$ , where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

A scalar has only magnitude (e.g., temperature), while a vector has both magnitude and direction (e.g., velocity).

The standard form of the equation of a hyperbola is $$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$$ or $$\frac{(y-k)^2}{b^2} - \frac{(x-h)^2}{a^2} = 1$$ .

The area of a circle is given by the formula $$A = \text{π}r^2$$ , where r is the radius.

A parabola is a conic section that is formed by the intersection of a right circular cone and a plane parallel to its side.

The sum of the interior angles in a triangle is always 180 degrees.

The distance between two points (x1, y1) and (x2, y2) is given by $$d = \text{√}((x2 - x1)^2 + (y2 - y1)^2)$$ .